It has been noted that both QBM and the scattering model yield the same dynamics in the limit of an environment dominated by long-wavelength (low momentum) and small central particle displacements. Their respective master equations reduce to the form originally derived by Joos and Zeh, which is itself in Lindblad form [1]}. This provides the motivation to construct the conditional wave theory corresponding to this important model. Consequently, a nonlinear equation of motion for the marginal wavefunction has been derived [2]}, possessing a logarithmic non-linearitypossessing a logarithmic non-linearity which predicts the same evolution for as the Joos-Zeh master equation (JZME) for Gaussian states.
